Abstract: In ultrasonic nondestructive inspection of large-diameter pipes, longitudinal cracks can be detected more efficiently by using guided circumferential waves. Based on linear three-dimensional elasticity，an orthogonal polynomial approach is used for determining the guided circumferential waves in homogeneous infinitely long orthotropic hollow cylinders. Results are compared with those published earlier to check up the accuracy and applicability of this polynomial approach. Guided circumferential wave dispersion curves for unidirectional composite pipes under different fiber intensity are calculated, and the effect of the variety of the fiber intensity on dispersion curves is shown. Finally, the guided circumferential wave dispersion curves for orthotropic pipes under different ratios of outer radius to thickness are calculated and the inherited influence of the variety of ratio on the dispersion curves is discussed.